Figure 1 - uploaded by Emmanuel Frénod
Content may be subject to copyright.
Source publication
The achievement of a project requires tools to monitor and adjust its evolution over time. Rather than to check at mid-term whether the objectives will be achieved or not, and adjust them, it is interesting to develop a control tool in order to effectively conduct the project's objectives. In this paper, we improve the continuous-in-time financial...
Contexts in source publication
Context 1
... order to test the efficiency of the filters introduced in Section 4.1, we build a class of periodic signals perturbed by some oscillations as shown in Figure 1, and we study the ability of filters to eliminate this oscillations. The goal is to estimate an original signal X from a perturbed version of X called Y and modeled as: ...
Similar publications
In the previous papers of Frénod & Ménard & Safa and Frénod & Safa we used the continuous-in-time financial model developed by Frénod & Chakkour, which describes working of loan and repayment, in an optimal control theory framework to effectively conduct project objectives. The goal was to determine theoptimal loan scheme taking into account the ob...
Citations
... In this section we extend the continuous-in-time financial model described in [1] [2] [3] in order to take into account the possibility of saving. The time domain is interval [ ] 0, Θ , where 0 Θ > is the lifetime of the project. ...
In the previous papers of Frénod & Ménard & Safa and Frénod & Safa we used the continuous-in-time financial model developed by Frénod & Chakkour, which describes working of loan and repayment, in an optimal control theory framework to effectively conduct project objectives. The goal was to determine theoptimal loan scheme taking into account the objectives of the project, the income and the spending. In this article, we enrich this con-tinuous-in-time financial model to take into account possibility of saving. Then we propose two new optimization problems involving this model. The first one consists in finding a loan scheme minimizing the cost of the loan for a project, together with the time to achieve its objectives. The second problem consists, from given loan, saving and withdrawal schemes, to findingoptimal variants of them. We have built a mathematical framework for the optimal control problem which consists to solving a constraint optimization problem. We have used Simplex algorithm to solve the first optimization problem and the quadratic programming for the second one. The simulations’ results areconsistent with the theoretical part and show the performance and stability of our approach
... We refer to Frénod & Safa [2,4,3], which improve one of the continuous-in-time financial models built in the present paper incorporating in it elements of control theory in order to determine the optimal loan scheme that achieves desired goals and that satisfies imposed constraints. ...
In a continuous-in-time model, there is an important financial quantity called Loan which cannot be determined directly in terms of algebraic spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a numerical method to concentrate a measure as a sum of Dirac masses.
... We refer to Frénod & Safa [2,4,3], which improve one of the continuous-in-time financial models built in the present paper incorporating in it elements of control theory in order to determine the optimal loan scheme that achieves desired goals and that satisfies imposed constraints. ...
In this paper, we construct a continuous-in-time model which is designed to be used for the finances of public institutions. This model is based on using measures overtime interval to describe loan scheme, reimbursement scheme and interest payment scheme; and, on using mathematical operators to describe links existing between those quantities. The consistency of the model with respect to the real world is illustrated using examples and its mathematicalconsistency is checked. Then the model is used on simplified examples in order to show its capability to be used to forecast consequencesof a decision or to set out a financial strategy.
In this paper, we study the inverse problem stability of the continuous-in-time model which is designed to be used for the finances of public institutions. We discuss this study with determining the Loan Measure from Algebraic Spending Measure in M([t I , Θ max ]), and in L 2 ([t I , Θ max ]) when they are density measures. For this inverse problem we prove the uniqueness
theorem, obtain a procedure for constructing the solution and provide necessary and sufficient conditions
for the solvability of the inverse problem in L 2 ([t I , Θ max ]).
